Directionally solidified (DS) superalloy castings are characterized microstructurally by either a columnar grain or single crystal structure. During the casting process, gas is sometimes entrapped within the casting mold, which can result in the formation of pores in the solidified casting. Researchers have known for some time that the closure of such porosity by hot isostatic pressing (HIP) improves the mechanical properties of DS castings. See, for example, Jablonski and Sargent, "Anisotropic Fatigue Hardening of a Nickel Base Single Crystal at Elevated Temperatures," Scripta Metallurgica, Volume 15, Page 1003, 1981. The HIP process described by Jablonski, et al is typical of the processes generally used throughout the industry, and is characterized by a substantially simultaneous increase of temperature and pressure from ambient conditions to a desired maximum temperature and pressure. The casting being HIP'd is then held at such maximum temperature and pressure for an extended period of time, usually in the range of about 2-10 hours, to close all of the as-cast porosity. The extended period of time at which DS castings are held at elevated temperature and pressure results in a significant addition to the cost of the casting. But, even with extended holds, complete closure of as-cast porosity does not always occur. Further, recrystallization of the casting has been observed to take place with some HIP cycles used in the industry. Recrystallized grains are particularly undesired in HIP'd DS castings, since such grains can act as fatigue fracture initiation sites. As a result of such concerns, the industry needs a HIP process which is less expensive to carry out and less prone to result in recrystallization than processes presently used.